$\text{The percentage distribution of the number of tires of different brands produced in a year by a certain factory is shown in the given pie chart.}$

$\text{The total number of tires sold is}1350.$

$\text{What is the difference between the average number of Avon and Firestone tires sold together and the average number of Good year and Dunlop tires sold together?}$

The correct answer is 54.

From the pie chart showing the percentage distribution of tire sales, we can observe the following data points for each brand:
- Avon = 21%
- Firestone = 14%
- Dunlop = 15%
- Good year = 12%
The total number of tires sold is given as 1350.

Step 1: Calculate the average percentage of Avon and Firestone tires sold together.

$\text{Average percentage (Avon \& Firestone)}=\frac{21\%+14\%}{2}=\frac{35\%}{2}=17.5\%$

Step 2: Calculate the average percentage of Good year and Dunlop tires sold together.

$\text{Average percentage (Good year \& Dunlop)}=\frac{12\%+15\%}{2}=\frac{27\%}{2}=13.5\%$

Step 3: Find the difference between the two average percentages.

$\text{Difference in percentage}=17.5\%-13.5\%=4\%$

Step 4: Calculate the actual difference in the number of tires sold.

$\text{Required Difference}=4\%\text{of}1350=\frac{4}{100}\times 1350=54$

Thus, the difference between the average number of Avon and Firestone tires sold together and the average number of Good year and Dunlop tires sold together is 54.